Example of a Triad Solution

A boundary survey is required of Lot "B" (below) to re-establish the missing corners. The coordinates of the map corners and the found monuments are retrieved from an ASCII (plain text) data file. See the following explanation of a sample printout (the Program Manual contains a detailed example)

 

********************** STEP ONE: INITIAL SOLUTION *********************

The record map is best fit to the five found monuments using the coordinates of common points. The largest error or residual is from the calculated position of #403 to the found monument #3 shown below as *181 in azimuth (S 1W) 0.81'. The best rotation and scale is determined with a 68% probable error indicated by the Standard Deviation.

Map Pts
Field Pts
Rectangular Differences
Polar Differences
System 1 to
System 2
North (Lat)
East (Dep)
N. AZIM
DIST
"402
"2
"-.004
"+.104
"92°
".104
"*403
"3
"-.809
"-.010
"*181°
"*.809
"404
"4
"+.475
"+.447
"43°
".653
"406
"6
"+.225
"-.137
"328°
".263
"407
"7
"+.113
"-.404
"286°
".419

Standard Deviation of the latitudes and departures = 0.39
Scale Factor = 1.00004129
Standard Deviation = .00038340
Rotation = - 1 09' 54.3"
Standard Deviation = 0 01' 19.1"


 

********************* STEP TWO: BLUNDER DETECTION*********************

This option determines the largest error that would remain after rejecting each of the found monuments indicated below. Rejecting #3 will reduce the largest error in the Initial Solution from 0.81'at #3 (above) to *0.13' at #6. The rotation and scale that would result follow on the same line.

REJECT
POINT #
MAXIMUM RESIDUAL
ROTATION
SCALE
N. AZIM
DIST -> PT #
2
181°
.79
3
-001° 10' 07"
1.000059
* 3
138°
*.13
* 6
-001° 09' 29"
.999336
4
88°
.45
2
-001° 10' 50"
1.000368
6
180°
.72
3
-001° 09' 42"
1.000090
7
181°
.66
3
-001° 09' 21"
1.000237

* It can be seen by inspection that the best solution will be obtained after rejecting #3. Triad will automatically search and report this fact.

 

********************* STEP THREE: FINAL SOLUTION ********************

Point #3 is rejected by setting the pair 403, 3 "FREE". The solution is re-computed to best fit the remaining monuments. The calculated corner positions now fall between 0.06' to 0.13' of the found monuments as shown below.

Map Pts
Field Pts
Rectangular Differences
Polar Differences
System 1 to
System 2
North (Lat)
East (Dep)
N. AZIM
DIST
402
2
+.055
-0.055
314°
0.08
403
3
-1.611
-.021
180°
1.61  FREE
404
4
+.037
+.049
53°
.06
406
6
-.096
+.085
138°
.13
407
7
+.004
-.079
272°
.08

Root Mean Square of the North and East Residuals = 0.06 (#3 excepted)
Scale Factor = 0.99933648
Standard Deviation = .00009303
Rotation = - 1 09' 29.9"
Standard Deviation = 0 00' 19.2"


 

***************** STEP FOUR: CREATE NEW COORDINATES *****************

New coordinates are computed for mapping and staking. To avoid conflicts in the coordinate file a value of 100 is added to the map point numbers for the new points computed in the field coordinate system.

Map Coordinates (input)
Field Coordinates (output)
PROBABLE ERROR
PT#
NORTH
EAST
PT#
NORTH
EAST
403
2748.923
5023.754
503
19315.877
39960.416
.13
405
3350.321
5042.829
505
19917.139
39967.325
.07

Note, there is an expectation at the 68% level of confidence that the computed positions of corners #403 and #405 are radially within 0.13' and 0.07'. This is useful in determining the reliability of the position or for an estimated corner search radius.

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